In many different areas of technology it is useful and important to obtain a focused beam of particles. A focused beam may be understood as a gas flow having a higher concentration of particles on the axis than off-axis. For example, such a particle beam can be fed in a vacuum chamber and directed as a collimated particle beam at a mass spectrometer or other apparatus that requires a well-defined input of particles for detection and/or measurement. Another example is particle deposition, where one seeks to focus the particle beam to predictably deposit a high-quality structure of particles on a substrate. Other uses for a particle beam are known in the art.
Particles smaller than 100 nm are often called nanoparticles. This definition partially overlaps with that of clusters, which is commonly used in the physics community to denote clusters of atoms or molecules in which the number of constituting elements can be counted, usually between 2 and 105 at/cl (atoms per cluster). They thus represent the smaller nanoparticles. The nanoparticles or clusters can be charged. Charged clusters are known as ionized clusters. A commonly accepted method in cluster physics is the expansion of a cluster-containing gas flow through a sonic orifice or nozzle into a region of much reduced pressure. However, the pumping action necessary to remove the gas molecules also removes a major part of the clusters and leads to a cluster beam with a large divergence. The reason for this is the fact that the clusters or particles are not focused to the axis of the flow before the expansion in the low-pressure region takes place. A technique to form a more focused beam is the application of a skimmer (an orifice placed to extract only a small part of the flow, effectively reducing the beam divergence. A second skimmer can further reduce the beam divergence and is called ‘collimator’ (described in ‘Cluster beam synthesis of nanostructured materials’ by P. Milani and S, Iannotta, Springer Series in Cluster Physics, 1999).
Narrow particle beams with small divergence angles are used in many applications to enhance transport efficiency, improve measurement resolution or deposit micropatterns precisely on a substrate. For example, collimated particle beams are often used as inlets to single particle mass spectrometers to efficiently deliver particles to the analyzing region, which is typically at a pressure about 8 orders of magnitude below atmospheric. The narrow beams also help to ensure that particles pass through the most intense portion of the laser beam used to vaporize and ionize the particles (Wexler and Johnston 2001). For similar reasons, collimated beams are useful in cluster spectroscopy studies (Roth and Hospital 1994; von Issendorff and Palmer 1999) or for the analysis of heavy molecules such as proteins. Particle beams are also used in materials synthesis, whereby particles are deposited on substrates to produce ultrasmooth thin films by means of energetic cluster impact (Haberland et al. 1995a, b), to create three-dimensional microstructures (Akedo et al. 1998), or to implant large metal ions (Carroll et al. 1998).
Aerodynamic focusing is one mechanism that has been widely used to produce tightly collimated particle beams (Fernandez de la Mora and Riesco-Chueca 1988). Using the aerodynamic lenses first designed by Liu et al. (1995a, b), nearaxis particles can be focused onto a single streamline in principle. An aerodynamic lens system typically consists of three parts: a flow control orifice, focusing lenses, and an acceleration nozzle. The choked inlet orifice fixes the mass flowrate through the system and reduces pressure from ambient to the value required to achieve aerodynamic focusing. The focusing lenses are a series of orifices contained in a tube that create converging-diverging flow accelerations and decelerations, through which particles are separated from the carrier gas due to their inertia and focused into a tight particle beam. The accelerating nozzle controls the operating pressure within the lens assembly and accelerates particles to downstream destinations. Aerodynamic lenses have been widely used in particle mass spectrometers (Ziemann et al. 1995; Schreiner et al. 1998; Schreiner et al. 1999; Jayne et al. 2000; Tobias et al. 2000), for material synthesis (Girshick et al. 2000), and for microscale device fabrication (Di Fonzo et al. 2000; Gidwani 2003).
Available designs for aerodynamic lenses effectively collimate particles as small as 30 nm. However, the focusing performance degrades dramatically as particle size drops below 20 nm. The main challenges in focusing sub-20 nm particles arise from their small inertia and high diffusivity. Because of their small inertia, nanoparticles tend to follow the gas streamlines very closely and only minor focusing can be achieved. The focusing of nanoparticles is further degraded by their high diffusivities, which lead to particle loss and beam broadening.
Several studies have been reported in which aerodynamic focusing was used effectively for very small particles. In their study of aerodynamic focusing of heavy molecules, Fernandez de la Mora et al. found that although Brownian motion of the heavy molecules seriously limited the focused beam width, molecular beams with a diameter of 0.35 of the nozzle diameter could be achieved (Fernandez de la Mora et al. 1989; Fernandez-Feria et al. 1991). They also used aerodynamic lenses to increase the resolution of impactors for nanoparticles, though detailed focusing performance of the lens systems was not reported (Fernandez de la Mora 1996; de Juan 1998; Fernandez de la Mora et al. 2003). In addition, significant focusing has been achieved using a novel focusing nozzle (herein referred to as the Italian focuser) for carbon clusters as small as 1.5 nm (Piseri et al. 2001; Tafreshi et al. 2002a, b; Piseri et al. 2004). This device utilizes two sharp turns of the aerosol flow path to focus particles to the centerline of the exit nozzle. A comparison of the Italian focuser and a typical aerodynamic lens assembly with 5 lenses (Liu et al. 1995a) is given in Table 1.
TABLE 1Comparison of the Italian focuser (Tafreshi et al. 2002a, b)and a typical aerodynamic lens assembly (Liu et al. 1995b).CarrierPressureFlow timeFocusinggas(Pa)(ms)Storange (nm)FocuserHelium1067-400030.11-6aLensesAir2671000.7-1.540-250
Note a: It is difficult to infer the focusing size range from their papers. The cluster size range is 1˜6 nm in their experiment.
The Italian focuser operates at higher pressure and with shorter particle residence time, both of which significantly reduce diffusion effects. Furthermore, this geometry has a smaller optimal Stokes number, which enables focusing very small particles onto the centerline. Compared to an aerodynamic lens system with multiple lenses, these simple sonic inlets focus a narrower particle size range, and the focusing performance has a stronger dependence on the initial radial position of particles. Note that lighter carrier gases (hydrogen or helium) were used in the above-mentioned nanoparticle (or heavy molecule) focusing experiments.
It is well known that Brownian motion is one of the major factors that limits the formation of nanoparticle beams with aerodynamic lens systems. There are several models in the literature that provide order of magnitude estimates of the particle beam width. Fernández de la Mora et al. estimated the effects of Brownian motion on beam widths downstream of a critical orifice (Fernández de la Mora et al. 1989). Fernández de la Mora further derived an asymptotic expression for diffusion-limited beam width in a periodic series of focusing lenses in the limit of Stokes number much smaller than unity (Fernández de la Mora 1996). Liu et al. developed an analytical expression for the diffusion-controlled particle beam width downstream of the accelerating nozzle assuming that all particles start from the axis with a frozen Maxwell-Boltzmann radial velocity distribution (Liu et al. 1995a, b). However, diffusion effects were neglected in most numerical simulations of particle trajectories through aerodynamic lens systems (Liu et al. 1995a, b; Zhang et al. 2004). The only work that incorporated Brownian motion in particle trajectory calculations was that by Gidwani (Gidwani 2003). Both Lagrangian and Eulerian approaches were used in that work to study particle focusing down to 10 nm. However, that lens assembly was not optimized for focusing sub-30 nm particles, and only the beam broadening inside the lenses was studied. The Lagrangian approach was followed to track particle trajectories in this work.
Existing technology can acceptably focus beams of particles of unit density as small as 30 nanometers (nm) in diameter. Some of these approaches involve the use of aerodynamic lenses, which may include a restriction disposed in the gas flow, the restriction having an aperture of a specific size. At smaller diameters, however, generally towards 20 nm, the focusing performance decreases. At sufficiently small particle sizes, there is currently no known aerodynamic lens that can provide acceptable focusing.